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It is challenging to measure the geometry distortion of point cloud introduced by point cloud compression. Conventionally, the errors between point clouds are measured in terms of point-to-point or point-to-surface distances, that either ignores the surface structures or heavily tends to rely on specific surface reconstructions. To overcome these drawbacks, we propose using point-to-plane distances as a measure of geometric distortions on point cloud compression. The intrinsic resolution of the point clouds is proposed as a normalizer to convert the mean square errors to PSNR numbers. In addition, the perceived local planes are investigated at different scales of the point cloud. Finally, the proposed metric is independent of the size of the point cloud and rather reveals the geometric fidelity of the point cloud. From experiments, we demonstrate that our method could better track the perceived quality than the point-to-point approach while requires limited computations.